The present study investigates how inertial effects and thermal dispersion interact to influence the initiation of convection in a fluid-saturated porous channel with horizontal throughflow. The channel is considered to be bounded by stress-free impermeable walls with the lower wall held at a constant temperature and the upper wall exposed to a uniform heat flux, creating a vertical temperature gradient that drives buoyant motion. The classical Darcy's law is extended with the Forchheimer term to account for the inertial effects within the porous matrix, while the energy equation accounts for thermal dispersion to capture the enhanced heat transport caused by velocity variations at the pore level. The resulting coupled ordinary differential equations are solved numerically using MATLAB's boundary value problem solver bvp4c. The analysis examines the influence of the various dimensionless parameters, including the Forchheimer coefficient, the Péclet number, the dispersion parameter, and the orientation of convection rolls, on the critical Rayleigh number and the corresponding wave speed at the onset of both stationary and oscillatory convection. The results reveal that increasing inertial resistance and thermal dispersion both act to stabilize the flow, delaying the onset of convection and suppressing the growth of perturbations. Additionally, the orientation of convection rolls plays a significant role: under forward throughflow, transverse rolls exhibit greater stability than longitudinal ones, whereas the reverse holds true for backward flow. Overall, this work highlights the intricate balance between advection, inertia, and dispersion in porous media, offering valuable insights relevant to heat management, filtration systems, and geophysical flow processes.
Veedhuluri et al. (Thu,) studied this question.